Corrected entry: Rose's mum phones the Alien hotline and tells them all about the Doctor. She says that he's called the Doctor and has a Blue Box, fair enough. But then she says he called it a TARDIS. Except that no one called it a TARDIS in front of her. The closest was Mickey calling it "that box thing"

Correction:What is seen on screen does not represent every second of real time, so therefore it is quite possible that the name was mentioned at some moment which was not seen on screen.

Doctor: So, that's the trap. Or the test or the final judgment, I don't know. But if I kill you, I kill her. Except that implies, in this big grand scheme of Gods and Devils, that she's just a victim. But I've seen a lot of this universe. I've seen fake gods and bad gods and demi-gods and would-be gods - out of all that - out of that whole pantheon - if I believe in one thing... Just one thing... I believe in her.

"Torchwood" is an anagram for Doctor Who. Russell T Davies came up with it during the filming of Series 1 to label the tapes in order to prevent theft and potential leakage, and decided to use the name in the show proper.